Divide the following complex numbers: $\dfrac{10 e^{23\pi i / 12}}{2 e^{\pi i / 12}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $10 e^{23\pi i / 12}$ ) has angle $\frac{23}{12}\pi$ and radius 10. The second number ( $2 e^{\pi i / 12}$ ) has angle $\frac{1}{12}\pi$ and radius 2. The radius of the result will be $\frac{10}{2}$ , which is 5. The angle of the result is $\frac{23}{12}\pi - \frac{1}{12}\pi = \frac{11}{6}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{11}{6}\pi$.